The Ideal Cut "Sweet Spot"
The round brilliant cut diamond evolved over several hundred years of diamond cutting. This style of cut stands above all others in importance and popularity for one most important reason. In the round brilliant, the finest cut quality or "make" brings out the best in the attributes of diamond beauty - brilliance, fire and sparkle.
Diamonds in a range of cut proportions seen as having greatest beauty possess the best combination of brilliance (in both its aspects of brightness and contrast), fire (rainbow hues) and scintillation (sparkle with movement). This is the essence of the ideal round brilliant.
Today, consumers in increasing numbers are looking for assurance that the round brilliant cut diamond they are purchasing is the best possible from the standpoint of optical performance or beauty. They look to the jewelers in bricks and mortar stores and on the Internet for proof of perfection of cut. In turn, the jewelers often look to the diamond grading laboratories or gemologist-appraisers for assistance in providing the consumer that proof of perfection of make.
On the surface, the laboratories today appear to be divided as to the finest or ideal make in the round brilliant diamond.
The AGS has concluded from their research that Tolkowsky was right, and the Tolkowsky Ideal, as defined in his landmark book, "Diamond Design", has the best optical performance, meaning that it possesses the best of the attributes of diamond beauty, brilliance, fire and scintillation.
GIA through their research and comparison testing has found "There is no one set of proportions that yields the most beautiful diamond." There is a range of combinations of proportion sets that are seen as top performers.
The range of angles and proportions that attain the GIA Excellent grade is larger than that of the AGS 0 Ideal. Their grade or measure of make has five levels. The highest is Excellent. Although there are significant differences, GIA's Excellent grade is better compared to the top two grades of the 11 grade AGS system, each being roughly the top 20% of the grades in both systems.
Several diamond cutting houses and retailers, some grading laboratories, and gemologists and researchers like myself set the bar for the ideal diamond make higher in some respects than either GIA or AGS. In a sense you could say we answer to a higher authority. That authority is our direct assessment of the diamond's optical performance in typical real world illumination circumstances.
Why these differing viewpoints? Can they be reconciled?
Consider the Commonalities
From the standpoint of the research and logic of each group, it can be argued that each is correct. More importantly, the argument can also be made that there are more areas of agreement among the cut grading systems than disagreement.
We believe the answer to the best round brilliant diamond make is to be found by examining the commonalities between the grading systems of all these groups rather than arguing their differences. Let us consider the commonalities.
The Diamond's Sweet Spot
In the sport of tennis, there is a term used for the small area near the racket center where the ball hits with the best, most consistent result or performance. This area is known as the tennis racket's "sweet spot". We can view the sweet spot in diamond cutting as that narrow range of diamond proportions and angles that result in the round brilliant's best, most consistent optical performance and beauty. We will show that an area of agreement among us all is the approximate location of the center of the round brilliant cut's sweet spot.
In tennis the best athletes use a racket with the largest sweet spot and aim to hit its center. In diamond design, the evolution of the ideal has lead cutters to that center of the largest sweet spot in round brilliant diamond cutting. The cutter's sweet spot is that range of diamond proportions and angles having the best optical performance. Today's cutters aim for the center of the round brilliant's sweet spot when they want to insure the best optical performance and beauty.
Seven parameters are used today to define the round brilliant cut. These parameters are the crown and pavilion main angles, the table size, the length of the lower girdle facets or halves, the length of the star facets, the girdle thickness and the culet size.
Morse Discovers the Ideal Crown and Pavilion Angles
Around 1860, Henry D. Morse, the first American diamond cutter, discovered the center of the diamond's sweet spot in two of the most important of the seven parameters. These are the crown and pavilion main angles. This was the greatest single stride in the evolution of what today is known as the ideal cut. A half-century later, the mathematician and diamond cutter, Marcel Tolkowsky, confirmed these angles with a theoretical math and physics argument in his book "Diamond Design".
Since that time, the term Ideal Cut has come to be associated with the angles and proportions of Tolkowsky's theoretical determination. These are a pavilion main angle of 40.75°, a crown main angle of 34.5° and a 53% table. This definition of the Ideal is incomplete because it addresses a theoretical center of the sweet spot for table size, crown and pavilion angles but not their range, and because it only addresses 17 of the 57 important facets defining the round brilliant cut diamond.
The Center of the Range of Ideal
Because of the historical overemphasis on Tolkowsky's theoretical angles of 40.75° and 34.5° in association with Ideal, it is important to know that the five diamonds that Tolkowsky listed in his book as examples of maximally brilliant diamonds had pavilion angles from 40°-41°, and crown angles from 33°-35°. Additionally, Tolkowsky notes in his book that American writers credit Henry D. Morse with first cutting for "maximum brilliancy". The angles that Morse first discovered that were said by American writers like Frank B. Wade ("Diamonds", 1916) and Herbert Whitlock ("Proportions of the Brilliant Cut", 1917) to yield an ideal make had a range that centered on a 41° pavilion and a 35° crown.
Frank Wade, one of the American diamond experts that greatly influenced the thinking about the ideal cut in his era, said of Morse's angles that "Within the limits of one or two degrees there is little variation in brilliancy" To varying extents this accords with today's consensus that there is a range of appropriate angles and proportions producing ideal optical performance and beauty. Differences of opinion are principally in the amount of variation in angles and proportions from those of Morse and Tolkowsky that retain the finest brilliance, fire and sparkle.
Let's look at those variations and the center of the round brilliant cut diamond's sweet spot for not only the crown and pavilion main angles, but all seven of the parameters that define all the important facets making up the round brilliant cut. We will find that the center of the round brilliant cut's seven-dimensional sweet spot is remarkably close in all the cut grading systems, and is a commonality upon which all can agree.
Comparing the Centers of the Sweet Spots
Let's look at the GIA's Excellent range of crown and pavilion main angles in their 5 grade system compared with the top two grades in the AGS's 11 grade system. The GIA Excellent grade and the top 2 AGS grades both comprise the top approximately 20% of each lab's grading system.
Because of the interaction and interrelationship between the diamond's parameters, they must be considered in relation to each other. This is why both GIA and AGS provide charts for each table size showing the range of crown and pavilion main angle combinations that make up each grade.
Center of the Sweet Spot for the Table
Figure 1 is a chart showing, for each table size, the number of combinations of crown and pavilion main angles that may attain the top grade in GIA's and AGS's grading systems.
A visual assessment of these curves indicates that the center of the sweet spot of the table size is closest to 56% in both grading systems. These two graphs indicate that table sizes within 2% to 3% of the sweet spot center of 56% contain a majority of the best combinations of crown and pavilion angles.
Sweet Spot Center for the Crown and Pavilion Angles
Let us analyze the combinations of crown and pavilion main angles that get the top grades in each system for a 56% table. We can compare the center of their sweet spots with the Morse and Tolkowsky ideal angle combinations.
Figure 2 is the chart of GIA cut grade estimation for the 56% table. The "sweet spot" of potential Excellent combinations of crown and pavilion angles has as its center, indicated by the red spot, a pavilion main angle of 41.2° and a crown main angle of 34.0°. Shown in blue and green are the Tolkowsky angles of 40.75° and 34.5° and the Morse angles of 41° and 35°.
GIA "Axis of Excellent"
Also shown is the slope of roughly 4.5 to 1 that is the axis of the sweet spot for crown and pavilion angle, "the axis of Excellent". Notice that Morse's American Ideal angles are on that axis and Tolkowsky's angles are in the Excellent range and only slightly shallower by .25° in pavilion angle and .5° in crown angle. Although the GIA "axis of excellent" is shown as a line with a slope of 4.5 to 1, it has a width. It is not necessary to be exactly on that line in order to attain the Excellent grade. It is a trend line. The slope of this line indicates that a change in pavilion angle from either Morse or Tolkowsky's angles is best compensated by a 4.5 times change in crown angle in the opposite direction.
Figure 3 is the corresponding AGS cut grade estimation chart for a 56% table. The "sweet spot" of potential AGS 0 and 1 combinations of crown and pavilion angles has as its center, shown with the blue dot, a pavilion main angle of 41.1° and a crown main angle of 33.75°
This center of the sweet spot for the top 20% of the AGS cut grades has the same pavilion angle within a tenth of a degree and a crown angle that is within a quarter degree of the corresponding center of GIA's Excellent grade.
AGS "Axis of Ideal"
The axis of best angle combinations for the AGS 0 and 1, the "axis of Ideal", is also about the same 4.5 to 1 as the GIA's "axis of Excellent". Tolkowsky's angles fall directly on this axis of best angle combinations with Morse's American Ideal angles of 41° and 35° being just slightly steeper in crown angle and slightly deeper in pavilion angle than this axis. Notice that this "axis of ideal", although having the same slope as the GIA axis of Excellent, is much narrower and excludes Morse's ideal angle combinations from the top two grades.
So the target center for sweet spot of the best round brilliant cut based upon these charts would be Morse's 41° for pavilion angle and closer to Tolkowsky's crown angle of 34.5° at 34°. Both 41° and 34° are very close to both the angles of Morse and Tolkowsky. In proper combination with the other five parameters, this sweet spot center of 41° and 34° along with the angle combinations of Morse and Tolkowsky all have ideal beauty. What about the center of the sweet spot for the other 4 of the 7 parameters defining the round brilliant?
The Important Length of the Pavilion Halves
There is general agreement that it is the interrelationship of the individual proportions that determine the diamond's performance and beauty. We can explore the ranges of the other parameters in the context of the best table size, crown and pavilion angles. Right up there in importance with crown angle and pavilion angle is the length of the pavilion halves or lower girdle facets.
In the late 19th century and in earlier times, the area of the pavilion occupied by the main facets dominated the diamond's reflection pattern, because the relatively smaller pavilion halves extended less than half the way to the culet. In the early 20th century in his book "Diamond Design", Tolkowsky indicated that the high-class brilliant had lower halves two degrees steeper than the pavilion mains. This results in a length of the lower halves of about 60%, which was a significant increase from earlier times.
During the 20th century, the pavilion halves were further increased in length with consequent increase in their area and influence on the diamond's beauty. The motivation for this increase in the length of the halves was the increased scintillation the larger halves provide. However, a consequence of the increase in the halves in order to favor scintillation was a decrease in the size of the mains. This brought an accompanying reduction of the desirable properties of large flash sparkle and fire that come from larger mains.
An attractive balance between the areas occupied by the mains and halves is necessary for the ideal cut to retain on one hand the large flash sparkle and fire that was the hallmark of the early ideal, and on the other hand, benefit from the greater scintillation of the modern round brilliant.
We have found that the best balance between the area of the main reflections and the area of the halves is obtained with a 75% to 80% length of the halves. The range of possible GIA Excellent lower girdle lengths is 70% to 85%. Both ranges have as the same 77.5% as the center of the sweet spot of lower girdle lengths.
Agreement on the Parameters of Girdle and Culet Size
There is general agreement on the two least important parameters of the seven that define the round brilliant cut. These are the girdle thickness and culet size. The noticeably large culets of the past are today known to detract from diamond beauty. They have been minimized or eliminated in the modern round brilliant. The girdle thickness is kept thin to medium to insure against chipping, and to avoid the diamond's apparent size (called "spread") from appearing noticeably smaller than normal.
Sweet Spot Center of the Star Length
That leaves just the star length as the remaining parameter to consider. In the context of the table size and crown main angle, the star length determines the angles of the star facets and the crown halves or upper girdle facets. Although having less impact on diamond beauty than the pavilion mains and halves, the angle of the crown halves (set by the star length) has an influence on the diamond's brilliance. Star lengths of 45% to 65% have the potential to receive a GIA Excellent cut grade. This makes 55% the center of the GIA sweet spot for star length. This accords with the practice of today's cutters of the modern ideal who find that the best round brilliant optical performance is obtained with the star facet length between 50% and 60%.
Summary of the Seven-Dimension Sweet Spot Center
In the round brilliant cut, ideal beauty is attained in the narrow range around the sweet spot center, where the ideal cut possesses an even distribution of brilliance, fire and sparkle in typical illumination circumstances. An essential part of the essence of ideal is the balance in optical performance between the properties of the reflections from the pavilion main facets and those from the lower girdle facets (the pavilion halves).
Factoring in Morse's and Tolkowsky's ideal angle combinations with the GIA and AGS parameter centers and the knowledge gained from our direct assessment, we can conclude that the seven-dimensional sweet spot center for the ideal round brilliant listed in order of parameter importance is:
- Pavilion main angle = 41°
- Pavilion halves length = 77%
- Crown main angle = 34.5°
- Table size = 56%
- Star Length = 55%
- Thin to Medium girdle
- Pointed culet
This multidimensional sweet spot center accords very well with our understanding of the parameters that yield the essence of ideal beauty. Our understanding is based upon direct assessment of the diamond's optical performance in typical real world illumination circumstances. There remain many important differences among the various grading systems, but we can all agree upon the center of the ideal cut diamond's sweet spot. Both Henry Morse and Marcel Tolkowsky would be pleased with today's ideal round brilliant cut, which evolved from their early key contributions to the art and science of diamond fashioning.
